If luck isn't random each day, what affects my character's different types of luck? Can I turn a type of luck around in a given day?
Luck is largely affected by Feng Shui and Lucky items. Thonky has a detailed article on the matter.
Taking Katrina's suggestion is also believed to improve luck but I don't have any firsthand knowledge of how well that works.
Every so often Katrina will visit your town. She might say that bad luck is in the future and a specific item will help. If you have it (like if it is clothing) then wear it, you never know, something nice might happen. However sometimes you can get those random bad luck days; don't worry, all that happens from what I've experienced is when you run your character will trip, look up the river glitch in youtube to find the advantage to this. Also in the accessories section in Able Sisters, there may be a King-Tut mask on sale. Be aware this does also give you the "bad luck". But if you want to glitch into your river, this item works too. Unless a fortune from Katrina, I'm not sure you can change your luck around. Hope I helped :)
I'm not positive, but I think the general things you say to the cat when you first start may affect this. Once, when I picked most of the bottom options, I had generally terrible luck. however, I had good physical and bell drops. When I picked all top options, it was the opposite. Item and friendship were high. There could be some hidden variables, like house location and battery that nobody knows about, but I'm confident on your picks being a part. (I never changed clothes or decorated my house.)